[en] In 1963, Hodgkin and Huxley obtained the Nobel Prize to have shown that the electrical activity of a neuron could be modelled by an electrical RC circuit containing non-linear conductances. This discovery made it possible to reproduce the electrical behaviour of neurons with a level of detail that has steadily increased over the last fifty years as new quantitative knowledge became available about the specific ionic currents that regulate the activity of a given neuron. But models with too many details are often non-robust and too complex for analysis. As control engineers need simplified models for control design, experimental neurophysiologists are in need of models that are amenable to sensitivity and robustness analysis, beyond the mere simulation of a given neuronal behaviour recorded experimentally.
The Purkinje cell has been studied for over hundred years because its large dendritic tree enables to recognize it easily with a microscope. This neuron exhibits a bistability between a stable hyperpolarized down-state and a stable depolarized spiking state. It is one of the first discovered neurons, however its electrical behaviour is not well understood so far. The principal question of the thesis is to model the electrophysiology of the Purkinje cell to advance the understanding of its regulation mechanisms. More particularly, the objective of the thesis is to explore recent work about the role of the calcium current in neuronal excitability as a possible mechanism underlying the bistability observed in the Purkinje cell.
The electrical activity of the Purkinje cell is reproduced in this thesis thanks to a reduced physiological model which can be seen as an intermediate between a detailed model with dendritic compartments and an abstract model of bistability. This novel model is the main contribution of the thesis. Its main ingredients are on the one hand a fast sodium current and a slow potassium restorative current whose particular kinetics account for the up-state excitability, and on the other hand a slow regenerative calcium current and an ultraslow calcium-dependent potassium current for bistability.
The proposed model suggests several implications. First, a complex compartmental model seems unnecessary to reproduce the electrophysiology of the cell, although the profuse dendrites are an important characteristic of the Purkinje neuron. Secondly, the Purkinje neuron appears to be regulated by the same mechanisms as other bistable neurons such as the thalamocortical (TC) or subthalamic nucleus (STN) neurons. Its behaviour depends on the same feedback mechanisms (a fast regenerative sodium current, a slow restorative potassium current and a slow regenerative calcium current), event though the temporal signature is markedly different because of the specific channel kinetics primarily of the slow potassium current. Finally this novel model makes the Purkinje cell modelling amenable to robustness and modulation studies, as recently shown for similar neurons.
